Topic
Modal operator
About: Modal operator is a research topic. Over the lifetime, 1151 publications have been published within this topic receiving 22865 citations. The topic is also known as: modal connective.
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TL;DR: This paper shows that certain operators that are usually regarded as extra-logical concepts (Tarskian algebraic operations on theories, mereological sum, products and negates of individuals, intuitionistic operations on mathematical problems, epistemic operations on certain belief states) are simply the logical operators that were deployed in different implication structures.
Abstract: On a structuralist account of logic, the logical operators, as well as modal operators are defined by the specific ways that they interact with respect to implication. As a consequence, the same logical operator (conjunction, negation etc.) can appear to be very different with a variation in the implication relation of a structure. We illustrate this idea by showing that certain operators that are usually regarded as extra-logical concepts (Tarskian algebraic operations on theories, mereological sum, products and negates of individuals, intuitionistic operations on mathematical problems, epistemic operations on certain belief states) are simply the logical operators that are deployed in different implication structures. That makes certain logical notions more omnipresent than one would think.
9 citations
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9 citations
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10 Dec 2020
TL;DR: The results show that some of these problems posed by the English non-modal operators to the undergraduate level students of Hazara University, Mansehra, Pakistan were caused by the intervention of some of grammatical concepts like tense, aspect, back shifting and voice.
Abstract: This study focuses on the problems posed by the English non-modal operators to the undergraduate level students of Hazara University, Mansehra, Pakistan. The data was collected from hundred students selected through non-random and convenience sampling technique. A proficiency test was used as a tool for data collection. The test was focused on all the uses of non-modal operators. The results show that some of these problems were caused by the intervention of some of grammatical concepts like tense, aspect, back shifting and voice. While some grammatical operations like negation, interrogation and insertion/omission had no role and so were found comparatively easy. These operators when used after wh-word such as when, while, before and if posed difficulty for the subjects. Similarly, different forms such as nontensed form and uses such as dynamic and non-dynamic of non-modal operators were also problematic for the subjects. The highest frequency of error was found in the use of non-model operator for emphasis and surprise. However, the degree of difficulty posed by non-modal operators in idiomatic expressions was not significant.
9 citations
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TL;DR: This study provides evidence that modal semirings are capable of handling a wide variety of (multi-)modal logics in a uniform algebraic fashion and links it to predicate transformer semantics, in particular to demonic refinement algebra.
Abstract: The aim of algebraic logic is to compact series of small steps of general logical inference into larger (in)equational steps. Algebraic structures that have proved very useful in this context are modal semirings and modal Kleene algebras. We show that they can also model knowledge and belief logics as well as games without additional effort; many of the standard logical properties are theorems rather than axioms in this setting. As examples of the first area, we treat the classical puzzles of the Wise Men and the Muddy Children. Moreover, we show possibilities of handling knowledge update and revision algebraically. For the area of games, we generalize the well-known connection between game logic and dynamic logic to the setting of modal semirings and link it to predicate transformer semantics, in particular to demonic refinement algebra. We think that our study provides evidence that modal semirings are capable of handling a wide variety of (multi-)modal logics in a uniform algebraic fashion.
9 citations
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01 Jan 2007
TL;DR: In this article, it is argued that a way to escape those problems is to redefine revision in a way that seems appropriate for this semantically richer context, and the approach can be extended to the case of multiple agents.
Abstract: Dynamic doxastic logic (DDL) is the modal logic of belief change. In basic DDL a modal operator [*?] carries the informal meaning “after the agent has revised his beliefs by ?” or “after the agent has accepted the information that ?”; it is assumed that the arguments of the star operator * are pure Boolean formulae. That assumption is discarded in full DDL where any pure doxastic formula may be an argument. As noted by other authors, a straight-forward extension of the theory from basic DDL to full DDL invites problems of the kind first discussed by G. E. Moore. In this paper it is argued that a way to escape those problems is to redefine revision in a way that seems appropriate for this semantically richer context. The paper deals only with the one-agent case, but the approach can be extended to the case of multiple agents.
9 citations